Galactic Super Massive Binary Black Hole Mergers

Galactic Super Massive Binary Black Hole Mergers

Galactic Super Massive Binary Black Hole Mergers

Dr. Peter BerczikAstronomisches Rechen-Institut (ARI),

Zentrum für Astronomie Univ. Heidelberg, Germany

Dr. Peter BerczikAstronomisches Rechen-Institut (ARI),

Zentrum für Astronomie Univ. Heidelberg, Germany

[email protected]@ari.uni-heidelberg.de

Second RSDN meeting, 25-27 Nov. 2005, Hoher List, Germany

Second RSDN meeting, 25-27 Nov. 2005, Hoher List, Germany

Collaborators:Collaborators: David MerrittDavid Merritt, , Rochester Institute of Technology, NY, USA Rainer Rainer SpurzemSpurzem, ARI, , ARI, Zentrum fZentrum füür Astronomie Univ. r Astronomie Univ.

HeidelbergHeidelberg Gabor Kupi, ARI, Gabor Kupi, ARI, Zentrum fZentrum füür Astronomie Univ. Heidelbergr Astronomie Univ. Heidelberg Stefan Harfst, Stefan Harfst, Rochester Institute of Technology, NY, USA

David MerrittDavid Merritt, , Rochester Institute of Technology, NY, USA Rainer Rainer SpurzemSpurzem, ARI, , ARI, Zentrum fZentrum füür Astronomie Univ. r Astronomie Univ.

HeidelbergHeidelberg Gabor Kupi, ARI, Gabor Kupi, ARI, Zentrum fZentrum füür Astronomie Univ. Heidelbergr Astronomie Univ. Heidelberg Stefan Harfst, Stefan Harfst, Rochester Institute of Technology, NY, USA

Grants:Grants: AST-0206031, AST-0420920 & AST-0437519 from the NSFAST-0206031, AST-0420920 & AST-0437519 from the NSF NNG04GJ48G from NASANNG04GJ48G from NASA HST-AR-09519.01-A from STScIHST-AR-09519.01-A from STScI SFB-439 from the Deutsche ForschungsgemeinschaftSFB-439 from the Deutsche Forschungsgemeinschaft

AST-0206031, AST-0420920 & AST-0437519 from the NSFAST-0206031, AST-0420920 & AST-0437519 from the NSF NNG04GJ48G from NASANNG04GJ48G from NASA HST-AR-09519.01-A from STScIHST-AR-09519.01-A from STScI SFB-439 from the Deutsche ForschungsgemeinschaftSFB-439 from the Deutsche Forschungsgemeinschaft

Publications:Publications: Berczik, Merritt & Spurzem, 2005, ApJ, 633, 680, [astro-ph/0507260] Berczik, Merritt & Spurzem, in prep…

Berczik, Merritt & Spurzem, 2005, ApJ, 633, 680, [astro-ph/0507260] Berczik, Merritt & Spurzem, in prep…

Galaxy Collisions:Galaxy Collisions:

BH’s in galaxies (MW - Sgr A*):BH’s in galaxies (MW - Sgr A*):

Galaxy Collisions ≈ BH’s collisions:Galaxy Collisions ≈ BH’s collisions:

Multiple Massive Black Holes

NGC6240strong ongoing merger…

Multiple Massive Black Holes

NGC6240strong ongoing merger…

Future Observations:Future Observations:

Gravitational Wave Detection - LISAGravitational Wave Detection - LISA

Two of the strongest potential sources in the

low-frequency (LISA) regime are:

•Coalescence of binary supermassive black holes•Extreme-mass-ratio inspiral into supermassive black holes

Milosavljevich M. & Merritt D., 2001, ApJ, 563, 34Hemsendorf M., Sigurdsson S. & Spurzem R., 2002, ApJ, 581, 1256Chatterjee P., Hernquist L. & Loeb A., 2003, ApJ, 592, 32Makino J. & Funato Y., 2004, ApJ, 602, 93Laun F. & Merritt D., 2004, [astro-ph/0408029]Szell A., Merritt D. & Seppo M., 2005, [astro-ph/0502198]

Some of the previous works:Some of the previous works:

Dynamical Modeling Methods:Dynamical Modeling Methods:

Direct N-body method:

- As much as possible accurate…- Symmetry of the problem is irrelevant…- (-) Very compute intensive!!!

Basic idea of the N-body code:Basic idea of the N-body code:

ii a

dt

rd

2

2

ijij

jij r

r

mGf

)(

2/322

N

ijjiji fa

;1

Hierarchical Block Time StepsHierarchical Block Time Steps

Our own GRAPE+N-body1 parallel code:Our own GRAPE+N-body1 parallel code:

4th order Hermite scheme4th order Hermite scheme

ijij

jij r

r

mGf

)(

2/322

~N~N ~N^2~N^2

N

ijjiji fa

;1

GRAPE = GRAvity PipEGRAPE = GRAvity PipE

jjjj tvrm ;;;

iiii tvrm ;;;

GRAPE = GRAvity PipE – more detail…GRAPE = GRAvity PipE – more detail…

iii aa ;;

GRAPE6a - PCI Board for PC-Clusters, recent development of the University of TokyoGRAPE6a - PCI Board for PC-Clusters, recent development of the University of Tokyo

~128 Gflops for a price ~5K USDMemory for N, up to 128K particles~128 Gflops for a price ~5K USDMemory for N, up to 128K particles

GRAPE6a PCI boardGRAPE6a PCI board

•32 dual-Xeon 3.0 GHz nodes•32 GRAPE6a•14 TB RAID•Infiniband switch (10 Gb/s)•Speed: ~4 Tflops•N up to 4M•Cost: ~500K USD•Funding: NSF/NASA/RIT

RIT & ARI 32 node GRAPE6a clustersRIT & ARI 32 node GRAPE6a clusters

•32 dual-Xeon 3.2 GHz nodes•32 GRAPE6a•32 FPGA•7 TB RAID•Dual port Infiniband switch (20 Gb/s)•Speed: ~4 Tflops•N up to 4M•Cost: ~350K EUR•Funding: Vwagen/BW/ARI

RIT & ARI 32 node GRAPE6a clustersRIT & ARI 32 node GRAPE6a clusters

Parallel PP on GRAPE6a clusterParallel PP on GRAPE6a cluster

iiii tvrm ;;;

jjjj tvrm ;;;

iii aa ;;

NN

N/NpN/Np

NactNact


calccommtotal TTT

proc

totactcalc N

NNT

0068.05437.0 totact NN


procactcomm NNT

procNproc TN

T

1



X

Y

ZTwo equal-mass black holes near center of Plummer-model galaxy

Initial Conditions - I:Initial Conditions - I:

020.0

005.0

21

21

BHBH

BHBH

mm

mm

6.0ak

k

k

k

k

400

200

100

50

25

4

1

1

TOTE

MG

Some Theory:Some Theory:

Example: loss-cone around a binary black hole.

Stars scattered into the binary are ejected via the gravitational slingshot. The binary responds by shrinking.

In a real galaxy, the shrinking rate (d/dt)(1/a) would be limited by the rate of diffusion of stars into the loss cone.

binary black hole

θ

star

ta

1

N-body Integration of Binary Black Hole Dynamical Evolution

N

t

a

1

Full loss-cone Diffuse regime

Results – I (Plummer):Results – I (Plummer):

020.021 BHBH mm

Results – I (Plummer):Results – I (Plummer):

X

Y

ZTwo equal-mass black holes near center of King-model (W0=6) galaxy

Initial Conditions - II:Initial Conditions - II:

020.021 BHBH mm

6.0ak

k

k

k

k

400

200

100

50

25

4

1

1

TOTE

MG

8.1,2.1,6.0,3.0,0.0o

Results – II (King):Results – II (King):

Results – I (Plummer) + II (King):Results – I (Plummer) + II (King):

Double check of the Results:Double check of the Results:

Double check of the Results:Double check of the Results:

BH collisions?BH collisions?

If we scaled up our numerical results, for the typical galaxy bulge (~10^9 Mo & ~3 kpc: 10 Gyr = 130) we see that the BH’s separation never come closer ~1 –

0.1 pc…

For the typical BH’s mass (10^6 Mo) the “gravitational merging” regime start with ~10^-6

pc!!!

]pc[ M10

102

o6

72

BHBHBH

M

c

MGR

d ~10*R_BH

???

Initial data… Initial data… No equilibrium…No equilibrium… Higher initial eccentricity…Higher initial eccentricity…

New code: New code: εε=0=0 regularization (CHAIN - ?, KS - ?)…regularization (CHAIN - ?, KS - ?)…

Larger direct N simulations: Larger direct N simulations: AC neighbor scheme…AC neighbor scheme…

N-body + GAS (SPH)N-body + GAS (SPH) Hardware solution for SPH calculations (FPGA)Hardware solution for SPH calculations (FPGA)

Initial data… Initial data… No equilibrium…No equilibrium… Higher initial eccentricity…Higher initial eccentricity…

New code: New code: εε=0=0 regularization (CHAIN - ?, KS - ?)…regularization (CHAIN - ?, KS - ?)…

Larger direct N simulations: Larger direct N simulations: AC neighbor scheme…AC neighbor scheme…

N-body + GAS (SPH)N-body + GAS (SPH) Hardware solution for SPH calculations (FPGA)Hardware solution for SPH calculations (FPGA)

Possible way of “solution”:Possible way of “solution”:

First large direct N ~1M parallel GRAPE6a cluster First large direct N ~1M parallel GRAPE6a cluster simulations…simulations…

The BBH decay rate is N dependent! ~400K – 1M The BBH decay rate is N dependent! ~400K – 1M particle is already enough to have a near “diffuse” particle is already enough to have a near “diffuse” regime…regime…

The initial rotation of the host galaxy is very The initial rotation of the host galaxy is very important for the BBH orbital evolution. For larger important for the BBH orbital evolution. For larger rotation we see the clear “fixation” of decay rate… rotation we see the clear “fixation” of decay rate…

Some of the highly rotating models can produce the Some of the highly rotating models can produce the BBH with a very high eccentricity e~1. Possible BBH with a very high eccentricity e~1. Possible source of the low frequency GW (LISA)…source of the low frequency GW (LISA)…

First large direct N ~1M parallel GRAPE6a cluster First large direct N ~1M parallel GRAPE6a cluster simulations…simulations…

The BBH decay rate is N dependent! ~400K – 1M The BBH decay rate is N dependent! ~400K – 1M particle is already enough to have a near “diffuse” particle is already enough to have a near “diffuse” regime…regime…

The initial rotation of the host galaxy is very The initial rotation of the host galaxy is very important for the BBH orbital evolution. For larger important for the BBH orbital evolution. For larger rotation we see the clear “fixation” of decay rate… rotation we see the clear “fixation” of decay rate…

Some of the highly rotating models can produce the Some of the highly rotating models can produce the BBH with a very high eccentricity e~1. Possible BBH with a very high eccentricity e~1. Possible source of the low frequency GW (LISA)…source of the low frequency GW (LISA)…

Conclusions:Conclusions:

Thank you for attentionThank you for attention...... Thank you for attentionThank you for attention......

Documents

Galactic Super Massive Binary Black Hole Mergers